F. Andersson

Runaway acceleration during magnetic reconnection in tokamaks

In this paper, the basic theory of runaway electron production is reviewed and recent progress is discussed. The mechanisms of primary and secondary generation of runaway electrons are described and their dynamics during a tokamak disruption is analysed, both in a simple analytical model and through numerical Monte Carlo simulation. A simple criterion for when these mechanisms generate a significant runaway current is derived, and the first self-consistent simulations of the electron kinetics in a tokamak disruption are presented. Radial cross-field diffusion is shown to inhibit runaway avalanches, as indicated in recent experiments on JET and JT-60U. Finally, the physics of relativistic post-disruption runaway electrons is discussed, in particular their slowing down due to emission of synchrotron radiation, and their ability to produce electron–positron pairs in collisions with bulk plasma ions and electrons.

Damping of relativistic electron beams by synchrotron radiation

Relativistic electrons emit synchrotron radiation due to their gyro- and guiding-center motions in a curved magnetic field. In this article, the kinetic theory of relativistic electron beams is developed to account for radiation reaction by including the Abraham–Lorentz reaction force in the kinetic equation. As an application of this theory, the dynamics of runaway electrons is examined and a steady-state solution is constructed describing a balance between acceleration by the electric field, pitch-angle scattering, and radiation reaction. Furthermore, it is found that a beam of relativistic electrons can be slowed down by the combined effects of pitch-angle scattering and radiation reaction. This damping can be more efficient than ordinary collisional drag, and appears to explain the decay of post-disruption runaway currents in the Joint European Torus (JET) [R. D. Gill, Nucl. Fusion 33, 1613 (1993)].

Suppression of runaway electron avalanches by radial diffusion

The kinetic theory of runaway electron avalanches caused by close Coulomb collisions is extended to account for radial diffusion. This is found to slow down the growth of avalanches. An approximate analytical formula for the growth rate is derived and is verified by a three-dimensional Monte Carlo code constructed for this purpose. As the poloidal magnetic flux that is available to induce an electric field in a tokamak is limited, avalanches can be prevented altogether by sufficiently strong radial diffusion. The requisite magnetic fluctuation level is sensitive to the mode structure and the speed of the disruption. It is estimated to be δB/B∼10−3 for parameters typical of large tokamaks.

Runaway electrons and the evolution of the plasma current in tokamak disruptions

After the thermal quench of a tokamak disruption, the plasma current decays and is partly replaced by runaway electrons. A quantitative theory of this process is presented, where the evolution of the toroidal electric field and the plasma current is calculated self-consistently. In large tokamaks most runaways are produced by the secondary (avalanche) mechanism, but the primary (Dreicer) mechanism plays a crucial role in providing a “seed” for the avalanche. As observed experimentally, up to 50%–60% of the plasma current is converted into runaways in the Joint European Torus [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)], and the conversion is predicted to be somewhat larger in ITER [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)]. Furthermore, the postdisruption current profile is found to be more peaked than the predisruption current—so much, in fact, that the central current density can increase although the total current falls. It is also found that the runaway current profile easi...

Slowing-down dynamics of fast particles in plasmas via the Fokker-Planck equation

Abstract A detailed discussion is given of the effects of energy diffusion and pitch-angle scattering on the slowing-down dynamics of a beam of monoenergetic particles being released with unidirectional velocity. Approximate solutions are given for characteristic averaged quantities like the pitch-angle averaged distribution function and different physically relevant velocity moments. The relation to previous exact investigations is discussed.

The optimal journey from A to B

How fast can you comfortably travel between two points A and B? This question is formulated as a minimization problem of a functional where the discomfort is quantified in terms of the integral of the square of the acceleration between A and B. The problem is solved in terms of the corresponding Euler–Lagrange equation and approximately using a direct variational approach based on trial functions and Ritz optimization. The main purpose of the analysis is to introduce undergraduate students to variational calculus in an interesting and pedagogical way.

Requirements as a Means to Drive Innovation: A Reason-Based Perspective

Requirements and their management is a focused issue in industrial product development, as well as in systematic design methodology presented in literature. Reflecting current industrial practice ? typically involving a strong focus on efficiency issues such as the use of standard components, development lead-time, and productivity ? there is a risk that the consideration of innovation and product value is suppressed. This paper presents possible factors that facilitate the creation of innovative products. These factors, condensed, form a basis for a reason-based method that confronts requirements and solutions with innovation and value issues. A possible application of the proposed method is demonstrated using an industrial product development case.

Effects of Backscattering on One-Dimensional Electron Beam Transport

Abstract A consistent scheme is formulated for solving the two-way diffusion problem describing the effect of backscattering on the lateral diffusive spreading of an initially unidirectional beam of monoenergetic electrons. The potential of the method is demonstrated by presenting an approximate solution, which bridges previous solutions found in the asymptotic limits of small and large scattering lengths, respectively.